1 Synthesis Econ 109 Fall 2002 Looking Back
Jan 06, 2016
1
Synthesis
Econ 109 Fall 2002
Looking Back
2
Outline
• Themes: The Big Issues
• Economic Concepts
• Perspectives By Course Section– What We Learned– Why We Learned It– How We Can Use It
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The Big Issues• Looking Out for # 1
– answer: save and invest (Course: Part I)
• Can a country (or civilization) generate a surplus to finance military power and/or the arts and sciences?– Answer: Malthus- landowners squeeze the
peasants– Answer: Marx- capitalists squeeze the workers,
(Course: Part III)– Answer: Adam Smith- markets lead to
efficiency and general welfare
4
The Big Issues (cont.)
– Answer: Modern economists- population growth increases the labor force; saving and investing increases capital; capital deepening increases worker productivity; research and development promotes technologival change (Course: Parts II and III)
– Answer: Monopoly power squeezes consumers (Course: Part III)
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Is Globalization & Trade Good or Bad?• Good• trade permits
decoupling of production and consumption, i.e. promotes specialization
• growth in GDP per capita leads to more equity
• trade promotes competition and curbs monopoly power
• Bad• growth uses up world
resources• global warming• loss of forests• loss of clean oceans
and rivers (Course: Part IV)
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Is Capitalism a Good Economic System or Not? (Course: Parts II, III, IV)
• Good• if markets are
competitive, then economy is efficient
• Bad• instability, subject to
fear, decreases in consumption and investment, capital flight
• monopoly power exploits consumers, wastes resources, and corrupts democracy
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Economic Concepts• Economic Paradigm: A Way of Thinking
– #1 set out your options for choice– #2 value these options ( using market prices or
personal values or social values)– #3 optimize, i.e. pick the best choice
• Marginal Principle– set marginal benefit(revenue) equal to marginal
cost (if marginal revenue is constant then marginal revenue=average revenue=price)
• Reality Principle
• Scarcity and Opportunity Cost
• Diminishing Returns
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Concept Applications
• Economic Paradigm– buying a car; Lecture 2– supplying your time to the labor market: L.4– choosing the investments with the average rate
of return-risk tradeoff that is best for you: L5– crime (pollution)-consumption possibility
frontier, community choice of optimal crim (pollution) levels L.17
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Tools Applications• Keynesian Cross: L. 6, L. 7 & L. 10
• Production Possibility Frontier– Guns or Butter L. 8, L. 10– Agricultural goods or manufacturing goods L. 12– Ag. Or mfg. Goods: a closed economy vs. trade andan
open economy
• Demand and Supply– demand for mortgage credit: L. 3– demand & supply of funds in the bond market: L. 4– demand & supply of banking reserves: L. 9 & L. 10
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Tools Applications• Demand and Supply
– demand and supply of world copper L.14– demand and supply of pesos: capital flight from
peso L. 15– demand & supply of $, capital flight from the
baht L. 16– demand and supply of bahts, capital flight from
the baht L. 16– demand & supply of low-skilled labor
contrasted to demand & supply of high-skilled labor, the wage differential for skill L 16
11
Tools Applications• Production Function, wage bill, surplus L. 11
• Marginal product of labor (demand), supply of labor, surplus L. 12– demand & supply of labor: minimum wage L. 12– demand & supply of labor: capital deepening L.13– demand & supply of labor: technological change L. 13
• Consumer Surplus & Competitive Markets L. 13– consumer surplus, monopoly profit, and dead-weight
loss L.14
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Tools Applications• Lorenz Curve and Gini Coefficient: L.16
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Perspective
• What we learned
• Why we learned it
• How we can use it
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Part I: Personal Finance, Economics of Everyday Life
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Purchasing the Big Ticket Items: Cars and Homes
• Why: Need to be well informed about the important decisions in our lives
• What: cars and houses last a while, and a $ this year is equivalent to a $ next year times one plus the interest rate $(t) = $(t+1)(1 + r)
• What: cars depreciate physically and most cars depreciate economically
• What: houses depreciate physically and will likely appreciate in value in CA
16
Cont.
• What: mortgage payments on loans are front loaded with interest, so equity will build slowly
• What: Need to save for the down payments, so we need to budget our expenditures
• How to use this info: when the time comes, tools are available for free on the internet or at low cost in common software packages
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Tool: Income-Expense StatementTool: Income-Expense Statement
Income Amount Expenditure Amountown salary taxesspouse “ life insuranceinsurance carsdividends foodinterest clothingrent housingother otherTotal Total
Savings Equals Income Minus Expenditure
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Economic PrinciplesEconomic Principles• A dollar today is not the same as a dollar
tomorrow!– $10 today @ 6.9% = $10 * 1.069 next year
• The “opportunity cost” of spending your money is the foregone interest.
• The cost of buying the services of the car, neglecting operating costs:– depreciation: owning a new car– foregone interest
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Increasing the Length of the LoanTradeoffs
Increasing the Length of the LoanTradeoffs
• monthly payment amount decreases
• amount of total payments increases
• amount of total interest payments increases
• total interest as % of total payments increases
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Thinking About Problems:The Economic Paradigm
Thinking About Problems:The Economic Paradigm
• describing the alternatives to choose among
• pricing the alternatives
• choosing the best alternative
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The Economic Paradigmexample: buying a car
The Economic Paradigmexample: buying a car
• describing the alternatives to choose among– cash: the opportunity cost of losing interest– lease: depreciation included in payments– loan: sell the car to account for depreciation
• pricing the alternatives: valuation– Oscar Wilde- economists know the price of
everything and the value of nothing
• choosing the best alternative– best: lowest cost– possibly subject to a constraint: having the $
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What to Do with Those Savings• Why: investments that earn more will let
you buy your cars and house sooner• What: investments have two attributes,
average rate of return(the reward), a good, and variability in the rate of return(the risk), a bad
• What: You want the investment with the highest average rate of return for a given level of risk
• What: returns are equal to capital gains (losses) plus dividends
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Two UC Funds: Monthly Rate of Return, Sept 95 - Aug 01
-15
-10
-5
0
5
10
Se
p-9
5
De
c-9
5
Ma
r-9
6
Jun
-96
Se
p-9
6
De
c-9
6
Ma
r-9
7
Jun
-97
Se
p-9
7
De
c-9
7
Ma
r-9
8
Jun
-98
Se
p-9
8
De
c-9
8
Ma
r-9
9
Jun
-99
Se
p-9
9
De
c-9
9
Ma
r-0
0
Jun
-00
Se
p-0
0
De
c-0
0
Ma
r-0
1
Jun
-01
Year:Month
Ra
te
Equity Fund
Insurance Contract
An Example of Two Alternative Investments
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Return Versus Risk for Six UC Funds Sept 95-Aug 01
Money Market
Savings
Insurance
Multi-Asset
Bond
Equity
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00
Risk: Volatility
Av
era
ge
Re
turn
Tool: Efficient Portfolio- Most Return for Given Risk
Economic paradigm step1
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Economic Paradigm step 2: Valuation of Mean Return and Risk
Assumption: Mean Return is Good, Risk is Bad: U =U(M,R)
MeanReturn,M
Risk, R
better
worse
Iso - Preference CurvesA
B
C
Prefer B to A; Prefer B to C
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Economic Paradigm step 3: Choosing the Best Investment for You
Economic Paradigm step 3: Choosing the Best Investment for You
UC Funds: Mean Return Vs. Risk (Standard Deviation)
Equity
BondMulti-Asset
Money Market
Savings
Insurance
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50Standard Deviation
Mean
Retu
rn
Investor B: not very risk averse
Optimum for B
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Personal Earnings and Human Capital
• Why: Your major source of $ is likely to be income
• What: Your Earnings will depend upon– your ability– your knowledge– your work experience
• How: Hang in until you get your college degree
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Families: Average Income and Average Net Worth, 1995
Quintile Av. Income Av. Net Worth
Lowest 20% $8,032 $3,000
Second 20% $17,916 $14,600
Third 20% $28,965 $31,185
Fourth 20% $43,930 $51,133
Highest 20% $73,058 $118,171
Source: Consumer Federation of America
Even with wealth of $100, 000, at 5%, you earn only $ 5, 000 of incomeso you will need to work
2924 hours0 hours
Leisure(learning)
Earnings
$480
Opportunities for trading leisurefor earnings (income) at a rate,$20 per hour, the market wage,determined by your stock of human capital(step one of the paradigm: describing the alternatives for choice)
$ 0
Tool: Earnings Opportunities: Trading Time for Money
Economic Paradigm step 1
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24 hours0 hoursLeisure(learning)
Earnings
$480
$ 0
Iso-Preference Curves:You value all points on a curve equally
high
low value
high value
Depicting your tastes graphically
Tool: Your preferences (tastes) for 2 goods, income & leisure
Economic paradigm step 2
3124 hours0 hours
Leisure(learning)
Earnings
$480
$ 0
high
low value
high valueOptimum
15 hoursof leisure
$180for 9 hrsof work
Individual’s Supply of Labor
Putting the 2 tools together: explaining your supply of labor
Economic paradigm step 3
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Part Five: Economic Welfare and Public Policy
• Why: we need to consider the welfare of fellow citizens, not just me-me-me
• What: most folks that are poor are poor because they do not work
• What: most folks that do not work have a low level of human capital, i. e. the labor market places a low value on their time
• What: persistent pockets of poverty among female heads of households and their kids
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Cont.
• In the US, the rich are getting richer and the poor are getting poorer
• In the US economy, there is a growing earnings premium on ability, on education, and on experience, i.e. on human capital
• In the US, we can’t seem to get the poverty rate below 10%
• How to use this info: on public policy issues when you vote
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24 hours0 hours
Leisure(learning)
Earnings
$480
$ 0
high
low valueslope of the iso-preference curve through the 24 hour endowment is the lowest wage at which you are willing to work
$96
dropout is unwilling to work for $4/hr
Life does not offer very good options for the uneducated
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Poverty and Female Heads of Households
Lab10: Children, Poverty, and Politics: US Census Bureau: Poverty in the United States: 2000
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Percentage of Births Occuring Out of Wedlock, . White Women by Age Group, US .
0
5
10
15
20
25
30
35
1955 1960 1965 1970 1975 1980
Year
Perc
en
t
15-19
20-24
25-29
One Difficulty in Reducing Poverty: Adverse Social Trends
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Poverty and Youth
Lab 10: Children, Poverty, and Politics
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Trends in Shares of US Family Income .
0
10
20
30
40
50
60
19
70
19
72
19
74
19
76
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
Year
Perc
en
t
Top 5 %
Top 20 %
Bottom 40%
In the US, the Rich Get Richer and the Poor get Poorer
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Ratio of Median Earnings, Males: College Grad to High School Grad
Source: Economic Report of the President, 1997
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Source: Economic Report of the President, 1997
Growing Wage Differentials Between the Less Skilled and More Skilled:Less Demand for Less Skilled and More Demand for the More Skilled
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Cont.• What: In the world, developed countries
have a more equitable distribution of income than undeveloped countries, one of the positive consequences of growth
• What: In the world, political systems and history also count. Socialist countries and countries with mixed economies tend to be more equitable. However, their tax burden is also greater
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The Distribution of Income and Growth
Honduras
Jamaica
Brazil
Mexico
Malaysia
Hong Kong
Singapore
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 2000 4000 6000 8000 10000 12000 14000 16000 18000
GDP Per Capita, 1990
Gin
i Co
effi
cien
t
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Tool: Lorenz Curves for Hungary and Brazil
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http://www.worldbank.org/depweb/
Income Inequality Across the World
Lab 7, Ch. 23, Internet Exercises, World Bank Links
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Lab 7, Ch. 23, Internet Exercises,
“Taking a Look at the Level of Economic Development and Well-Being in Countries Around the World”
Link to Handbook of InternationalEconomic Statistics
Higher Tax Burden in France than in the US
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Part Two: Macroeconomics and the US Economy
• Why: because the economy affects your prospects for finding and keeping a job, the interest rate you pay on loans, and the return you get on your investments
• What: There are two ways to measure the size of an economy, National Income and National Expenditure or GDP (circular flow). They have to be the same, i.e. in equilibrium
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Cont.
• What: GDP is equal to consumption by consumers plus investment by firms, plus spending by government plus net exports ( exports minus imports)
• GDP = C + I + G + X - M
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: Chapter Twenty: Chapter Twenty• Conceptual Framework: Circular Flow
Firms
Households
Income Labor
Firms
Households
SupplyGoods
Demand Goods
Income Perspective Expenditure Perspective
Y = GDP
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Expenditure Perspective: OpenExpenditure Perspective: Open
Firms
Households
SupplyGoods
Demand Goods
Households: Consumption of Goods and ServicesFirms: Investment in Plant and EquipmentGovernment: Purchase of Goods and ServicesAll Three: Exports - Imports = Net Exports
Imports(puchases)
Exports(Sales)
Government
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Consumption, CInvestment, IGDP
National Income, Y
GDP = C + I +G
450
GDP = Y
Income = expenditureI.e. Y = GDP
TotalExpenditureGDP Line
AggregateExpenditure
Unemployment Rate Oct. 2000= 3.9%
Bust
Unemployment RateSept 2001 = 4.9 %
Graphical Tool: The Keynesian Cross
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US Postwar ExpansionsUS Postwar ExpansionsTrough - Peak Duration, MonthsOct. ‘45 - Nov. ‘48 37Oct. ‘49 - July ‘53 45May ‘54 - Aug. ‘57 39April ‘58 - April ‘60 24Feb. ‘61 - Dec. ‘69 106Nov. 70 - Nov. ‘73 36March ‘75 - Jan. ‘80 58July’80 - July ‘81 12Nov. ‘82 - July ‘90 92March ‘91 – March ‘01 121
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Cont.• What: In addition to fiscal policy, I.e
taxation policy and government spending, the US central bank, the Federal Reserve, engages in monetary policy
• What: the Fed can buy government securities on the secondary bond market (open market operations) and if it buys from a private bank, for example, credits this bank with reserves. This private bank can use any excess reserves over those required by the Fed to make loans to consumers and businesses. In turn these groups can spend.
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Cont.• What: the federal funds rate is the rate of
interest banks pay to borrow from one another. If the Fed increases the supply of reserves through open market operations, this results in a decrease in the federal funds rate.
• What: The central bank acts as a bank of last resort, lending money to private banks at the discount window, charging them interest at the discount rate.
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Impact of the Supply of Reserves on the Federal Funds Rate
Impact of the Supply of Reserves on the Federal Funds Rate
FFR,price ofreserves
quantity of reserves
Demand for Reserves by Banks
Supply of Reserves: Fed
55
Fighting Recession, the Fed Cuts the Federal Funds Rate from 6.5% in Dec. 2000 to 2.5% in Oct 2001
During the Same Period, the Fed Cut the Discount Rate from 6% to 2 %
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Part Three: Competition, Monopoly, and Public Policy
• Why: Growth in GDP per capita increases the standard of living for people and means that we can avoid the Malthusian trap and avoid Marx’s prediction of the increasing immiseration of the working class
• What: Growth depends on increasing worker productivity, i.e. output per worker or average product. Output per worker increases as capital per worker rises (capital deepening), including social infrastructure, and as technology improves
58
Cont. • What: Malthus believed that population
increases would devour any surplus in output, keeping peasants at a subsistence wage.
• What: Marx believed that capitalists would seek more profit by introducing labor saving machines, displacing workers and creating an army of the unemployed. This surplus of workers would keep wages at the subsistence level. Neither Malthus nor Marx foresaw capital accumulation and technological change saving the day.
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Cont.
• What: Because economic growth leads to prosperity, more and more countries are embracing free markets, capitalism, and international trade.
• How to use this info: You can stay up at night worrying whether science, engineering and technology will bail us out in the coming century, as it did in the past two, or whether Malthus and Marx will ultimately be right.
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GNP Per Capita, Growth Rates Around the World
61
Average, Marginal Product
Input, # of workers
APL
MPL1954
Things Improve with capital deepening:
Output perWorker
MPL1874
Labor Supply1874
Real Wage1874
L1874
Labor Supply1954
L1954
Real Wage1954
Output per workerincrease, shifting APL
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Capital Stock
Depreciation
NetInvestment-
GrossInvestment
+
Capital Formation
NationalSavings
63
Table 23.2
Source of Real GDP Growth, 1929-1982 (average annual percentage rates)
Due to capital growth 0.56 19 %
Due to labor growth 1.34 46 %
+ technological progress 1.02 35 %
Output growth 2.92 100 %
Source: Edward F. Denison, Trends in Economic Growth 1929-82
(Washington, DC: The Brookings Institution, 1985).
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Research and Development as a Percentage of GDP
Chapter 23, Figure 23.5
65
LATC
Optimal Size of Plant with Variable Returns to Scale
SATCIII
SATCIV
SMCIV
LMC
Quantity
pM
LATC
SMCIII
SD
Market(differentscale foroutput)
Reference: Lecture 14
66
The Social Cost of Monopoly: Example, Constant Returns to Scale
LATC = LMC
Market Demand
Competition Monopoly
Market Demand
LATC = LMCPM
Consumer Surplus
MR
QCOMP QMONOP
PM
Under monopoly, some consumer surplus is redistributed to the monopolist as profit, and some is lost to society
Profit
Dead Weight Loss
67
The Ghost of Malthus
68
Population Growth Rates Around the World
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Part Five(again): Economic Welfare and Public Policy
• Why: Economic growth and prosperity may not be unambiguously good. Growth may bring pollution as a byproduct. Free markets and free societies may have more deviant behavior.
• What: Societies must choose through their political system how much GDP to allocate to cleaning up the environment and how much GDP to allocate to fighting crime and keeping citizens and their property safe
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Tool: Crime (pollution) - Consumption Possibility Frontier
Consumption: good
Offenses (pollution): bad
The first step of the paradigm: the options for choice
Opportunity cost ofless crime
Minimum possible
71
Community Values Confront Reality:Crime (pollution) - Consumption Possibility Frontier
Consumption: good
Offenses (pollution): bad
The second step of the paradigm: pricing the options
Community preferences
Community wishlist
optimum
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The Developed Countries Are Increasing the Risk of Global Climate
Change
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The Developed Countries Are Also the Ones That Can Afford To Clean Up
Llad Phillips 76
Central Government Expenditure as a % of GDP, 1995
http://www.worldbank.org/depweb
74
Part Four: Trade, the Balance of Payments and the Global Economy
• Why: Globalization characterizes our times. World trade is stimulating economic growth, breaking down the barriers that protect inefficient domestic industries.
• What: Trade, or voluntary exchange, benefits both parties. Trade allows them to specialize on what they do best, rather than be self-sufficient, and specialization increases productivity. Trade permits the decoupling of production from consumption.
75
Cont.• What: Trade of goods and services may not
always be in balance however. Imports may exceed exports and countries, like people, may borrow to live a little higher on the hog. For people, this is often reflected by credit card debt. In the case of countries, we call them debtor nations.
• What: The danger in being a debtor nation is the possibility of capital flight. Foreigners who own a country’s bonds may sell them and then sell this country’s currency to buy their own, i.e. cash out and go home.
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Cont. • What: If the target country’s central bank
does not have sufficient reserves of foreign currencies to permit them to buy their own currency, and offset the effect of capital flight on the exchange rate, they will have to devalue their currency.
• What: A stable exchange rate means trade and economic activity is less risky.
• What: Currently, the only mechanism to offset capital flight and avoid international monetary crises is cooperation among central banks, arranging loans for the target.
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Growth in World TradeGrowth in World Trade
Source: Source: Economic Report of the President, 1997 Economic Report of the President, 1997
http://www.gpo.ucop.edu/catalog/erp97.htmlhttp://www.gpo.ucop.edu/catalog/erp97.html
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Around the World, Trade is Growing Faster Than GNP
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Agriculture
Manufactures
Trade Allows the West to Decouple Production & Consumption
Production Possibility Frontier, PPF
Regional Tastes:
Eastern Prices: Ag/ Mf = PMf/PAg
A
BC
QMf
QAg
CMf
CAg
Exports
Imports
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Capital FlightCapital Flight1. foreigners sell their Thai investments1. foreigners sell their Thai investments2. foreigners exchange their Baht proceeds for say dollars2. foreigners exchange their Baht proceeds for say dollars3. Demand for dollars shifts and price of the dollar in Bahts rises 3. Demand for dollars shifts and price of the dollar in Bahts rises
Bahts per US $Bahts per US $
quantity of dollarsquantity of dollars
demand for dollarsdemand for dollars supply of dollarssupply of dollars
Figure 1A: Before Capital Flight Figure1B: After Capital Flight
$ price of theEuro
Quantity of Euros
Supply of Euros
Demand for Euros
$/Euro
Quantity of Euros
Demand for Euros
$ price of theEuro
$/Euro
Part III. (45 points) Answer all three questions.
1. Suppose, in the future, countries in the European Monetary Union (EMU) lose
confidence in the attractiveness of the United States as a haven for their investments,
perhaps in part because US interest rates decline dramatically. Suppose this causes a
repatriation of money to EMU countries, and fewer Euros are supplied to the US and to
the foreign exchange
a. After capital flight, show the shift in the supply curve of Euros in Figure 1B.
b. Does the equilibrium quantity of Euros increase or
decrease?__decrease____________
c. Does the Euro appreciate or depreciate? __appreciate_______________
d. Illustrate the new exchange rate in Figure 1B.
e. If the U S Federal Reserve intervenes in the foreign exchange market using its
reserves of foreign exchange, which curve will shift, the demand curve for Euros
or the supply curve for Euros? __supply____________
2. Currently, for the third quarter of 2000, the economy is at full employment at $10.05
trillion(T) for GDP. Net exports, X-M, are in deficit at $-0.39 T and government
expenditures, G, are $1.75 T. So together, government expenditures and net exports are $
1.36 T. Note that the government is in surplus, i.e. expenditures exceed receipts from
taxes etc., so the government is absorbing purchasing power rather than generating it.
For the sake of simplicity, assume government expenditures and net exports do not vary with national
income, as illustrated in Figure 2.
In thinking about the prospects about a recession in 2001, the expenditure
emphasis is on the private domestic economy: consumers and business firms.
Figure 2: The Keynesian Cross and GDP Expenditure = National Income
GDP,ExpenditureComponentsIn $ Trillions
450
$10.05 T
G + (X-M) = $ 1.36 T
National Income
Full EmploymentNational Income, $10.05T
Total GDPLine
G + (X-M) < $ 1.36 T
Total GDP Line if C + I fall
a. Together, how many trillions must consumption and investment total at the full
employment level of national income? _____$8.69 T______________
b. Draw in the total expenditure (or GDP) line in Fig. 2, which increases with
national income, since consumption increases with national income, showing
its intersection with the GDP= National Income line at $10.05 T.
c. Suppose consumer confidence continues to weaken, and consumption and
investment expenditure fall. Illustrate the consequent shift in the total
expenditure (or GDP) line in Figure 2.
d. If the balance of trade deficit grows worse, and fiscal policy and government expenditure do not
change, illustrate the effect on the G + (X-M) line in Figure 2.
e. If all of these unfortunate things come to pass, what will happen to the unemployment rate? __it ___
___will_______ ___rise_____________.
3. The technology for electricity generation has increasing returns to scale and therefore a downward sloping long-
run average total cost (LATC) curve, as illustrated in Figure 3. These are the conditions for a natural monopoly.
Price perKilowatt Hour
LATC
Billions of Kilowatt Hours,q
Long Run Marginal Cost
Market Demand
Marginal Revenue
qR
pR
qM
pM
Figure 3: Market Demand and Long Run costs per Kilowatt Hour for Electricity
a. If the government deregulates electricity, as has happened in California, and
the monopolist is free to determine output and price, show in Fig. 3 the price,
pM, and the output, qM, the monopolist will choose.
b. Under government control of electricity, an efficient use of resources would
result from setting price equal to long run marginal cost (LMC) where LMC
crosses the demand curve. Why isn’t this a feasible price for the government
to set? The low price would benefit the consumer. _monopolist_________
_makes_____ _a_ __loss___________.
c. With government regulation of the electricity market, using average cost
pricing, the government could set long-run average total cost to price where
LATC crosses the demand curve. Illustrate this regulated price, pR, and
corresponding quantity, qR, in Fig. 3. Comparing, deregulation, with the
monopolist free to maximize profits, to regulation, is the consumer better off
or worse off? _better________ ___off_________( with regulation).
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Course Grading
Quiz 40Midterm 80Final 169Course 289
If you complete over 70 % of both the text Problems and Lab Exercises, then your course grade is increased by 1/3 grade point
87
Thursday, Dec. 12, 4:00-7:00 PM, Final, You will need a scantron sheet and #2 pencil.
• Good Luck